Tag Archives: Big Bang

Indirect Evidence for Dark Matter

I’ve already gone over some of the main pieces of evidence for the existence of dark matter. There are also a lot of more indirect reasons why we think dark matter should exist. I’ve already mentioned these in earlier posts, but here are some of the other measurements and models supporting the dark matter hypothesis.

Big Bang Nucleosynthesis

Using a model of the universe assuming the universe started in a very hot and dense state that expanded adiabatically, we can estimate the relic abundances of the lightest few isotopes, which are mostly produced here rather than in the centers of stars.

The abundances (typically ratios rather than absolute abundances) of objects thought to have compositions close to what’s left after BBN have been measured and have been found to match predictions quite well. There is some disagreement on lithium-7 but the lighter isotopes match predictions from BBN models.

While this doesn’t necessarily tell us that dark matter exists, it does help validate our model of the early universe. It also helps to further challenge models where the “dark matter” is really just some regular matter that we aren’t measuring for some reason.

Structure Formation

Large structures in the universe are believed to have coalesced out of small primordial density fluctuations. Matter is pulled into regions that start with a slight overdensity, leading that overdensity to keep increasing in magnitude. This eventually leads to dense (compared to the average density of the universe) objects like galaxies, clusters, etc.

It turns out that simulations suggest that a universe containing only regular matter will not lead to the structures we see in the universe. The clumps of matter will not form quickly enough. However, if the mass overdensities are made of dark matter, large gravitationally bound objects will form properly. The dark matter provides mass to increase the gravitational forces in these overdense regions but does not clump into compact objects. The compact objects are made of baryonic matter trapped by the dark matter’s gravitational forces.

Cosmic Microwave Background

Skymap of temperature fluctuations in the cosmic microwave background measured by Planck. Credit/copyright: ESA and the Planck Collaboration.

The CMB is the result of the photon-baryon fluid in the early universe (at a redshift around 1100) becoming transparent to photons. When the universe cools sufficiently, the baryonic atomic nuclei start capturing electrons, changing from charged ions to neutral atoms. This means that there are no (or at least few) charged particles left, so photons, which couple to electric charge, have trouble interacting with anything. The photons then are able to continue on without interacting with anything until we measure them billions of years later. The photons follow the standard blackbody spectrum, which is then redshifted until today where the spectrum corresponds to a temperature of 2.7 K (a few degrees above absolute 0) and peaks at microwave wavelengths.

The CMB is not uniform in the sky. It’s temperature is seen to feature tiny fluctuations in space. These can be seen as relics of oscillations in the photon-baryon fluid (to lowest order the different oscillatory modes do not interact with one another). The power spectrum tells us the strengths of these different modes. The properties of the modes (basically the size of the temperature fluctuations on different spatial scales) are related to the properties of the photon baryon fluid. So, we can extrapolate the composition of the early universe from the CMB power spectrum. Fits of a generic early universe model to the measured power spectrum show that a large fraction of the energy content of the early universe (and the current universe) appears to be from non-relativistic, non-baryonic dark matter. Measurements of other things such as Type Ia supernovae (a popular standard candle) help us refine our model, and everything points to the existence of dark matter.

 

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A Brief, Qualitative History of the Universe: Part I

Returning to my Physics for Non-Physicists series, I will temporarily switch to a new topic: cosmology. I’d like to talk about dark matter next, and a little knowledge about modern cosmology is necessary to understand some things about dark matter. As the title suggests, this discussion is meant to be qualitative and pretty brief. I may return to the subject in the future to discuss it in further detail, but that wouldn’t be for a while.

Introduction: The Expansion of the Universe

Many early physicists traditionally saw the universe as a static, fixed thing. However, by some time during the 20th century, astrophysicists were able to measure objects many millions of light years away from Earth. While the Milky Way galaxy contains huge numbers of stars gravitationally bound to one another, and the galaxy is even bound to other galaxies in a galactic cluster, it turned out that on large enough scales everything appeared to be moving away from us, as if in the distant past an enormous explosion sent all these things away from us.

That is not the whole story, though. It also seemed like on large enough scales, everything is moving away from everything else. In fact, the rate at which the distance between two objects is increasing is proportional to the distance between the objects. The proportionality constant is called Hubble’s constant. So, it almost seems like in the distant past this motion was set in motion by a huge explosion that existed everywhere all at once (the Big Bang).

It turns out that this is what we would expect if instead of what we might consider an explosion (a violent chemical reaction), the recession of everything from everything else were actually due to an expansion of space. So what does this mean? Consider an empty toy universe, where you can step outside the universe and place two test particles at some known distance. Also let these two test particles be noninteracting and have no relative velocity. If space expands or contracts uniformly, the distance between the particles will expand and contract as well, even with no forces acting on the particles. This may seem at first glance to violate Newton’s First Law (the Law of Inertia). It doesn’t. Many of the laws of physics describe local phenomena. It only matters that on a small enough (even infinitesimally small) scale the particles look stationary.

This expansion of space was something that was predicted by Einstein’s general theory of relativity (GR), first released in 1916. GR describes space and time as dynamical, rather than static, objects. The equations governing the dynamics of space and time are intrinsically related to the distribution of energy in the universe. In GR, the geometry of space and time give rise to gravity, which exerts forces on energy, which affects the geometry of space and time.

The Shape of the Universe

Then how do we go from GR (a local theory whose dynamics depends only on knowledge of what’s going on in some finite region of space) to talking about the history of the whole universe?

We first invoke the principles homogeneity and isotropy. Homogeneity means that on large enough scales (hundreds of millions of light years), everywhere in the universe looks the same. Obviously, we exist so homogeneity does not hold on all scales, but on truly cosmological scales we assume this to be true. Isotropy means that on large enough scales every direction looks the same as well. Thus, the universe has no preferred position and no preferred direction.

With these assumptions, we can easily deduce that on large enough scales, the small structures in the universe from the uneven distribution of mass/energy smooth out, leaving us with a universe that is smooth, homogeneous and isotropic. Everything else is just minor details. It turns out that there are then only 3 possibilities for the shape of the universe. Now consider a two-dimensional universe. In two dimensions, the 3 possibilities are a sheet (a flat/Euclidean universe), the surface of a sphere (positive curvature), or a shape similar to a potato chip (negative curvature). The positive curvature universe has a finite size, while a flat or negative curvature universe is literally infinite in size. Our universe must be shaped like the 3-dimensional analog of one of these.

It’s actually in principle possible to directly differentiate the 3 types of universes. The “shape” is characterized mathematically by what’s known as the metric tensor. The metric tensor defines the length of an infinitesimal line segment given some set of coordinates. The different geometries basically just have different (and non-equivalent) definitions of a straight line. In the 2D case, the line on a sheet is what we wold term a line. The “line” on the surface of a sphere is a great circle. If you could draw a perfect triangle and perfectly measure its angles, you would see that in a flat universe, the sum of the three angles is 180 degrees, in a positive curvature universe, the sum is greater than 180, and in a negative curvature universe, the sum is less than 180. Universes with non-zero curvature have some characteristic length scale governing the curvature. On scales much less than this scale, everything looks flat. As far as we can tell, the universe is flat, but this really just means that the characteristic length scale of the universe is very large.

The Observable Universe

Remember that two of the three global geometries of the universe are infinite in size. You may also know that we can only look so far away (a few tens of billions of light years). It seems to us like the universe really is finite. How do we reconcile these facts without just declaring the universe to have positive curvature?

Our best estimates of the age of the universe tell us that the Big Bang occurred 13.8 billion years ago. Light in a vacuum travels at speed of light (obviously), so in those 13.8 billion years, any given photon can only have traveled so far. Looking far away is also looking backward in time, so we can’t see farther away from us than the maximum distance light could have traveled throughout the whole age of the universe. It turns out that this distance is actually larger than 13.8 billion light years. The light traveled that far, but the objects have been pulled away from us since the light was emitted. We also can’t really see light from the Big Bang as at some point the universe was dense and hot enough to be opaque to light.

Basically, as long as the universe – or at least the universe as we know it – has a finite age, we will have a finite horizon beyond which we can never see.

That’s enough for today. I’ll continue later with discussions of the overall history of the universe and the thermal history of the universe.